Method for unsupervised sorting in real time of action potentials of a plurality of biological neurons

ABSTRACT

A method for unsupervised sorting, in real time, of action potentials of biological neurons by a network of artificial neurons including input, intermediate and output layers, the method according to which: the input layer receives an electrical signal measuring an electrical activity of biological neurons, the electrical signal having a variable amplitude as a function of action potentials emitted by the plurality of biological neurons over time; the input layer converts the amplitude of the electrical signal into a train of first spikes; the input layer transmits the train of first spikes to the intermediate layer; the intermediate layer converts the train of first spikes into a train of second spikes; the intermediate layer transmits the train of second spikes to the output layer; as a function of the train of second spikes, the output layer sorts each occurrence of each type of action potential present in the electrical signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to French Patent Application No.1654485 filed May 19, 2016, the entire contents of all applications areincorporated herein by reference in their entireties.

TECHNICAL FIELD OF THE INVENTION

The technical field of the invention is that of the sorting of actionpotentials of biological neurons. The present invention relates to amethod for unsupervised sorting in real time of action potentials of aplurality of biological neurons.

A field of application of the present invention is notably that ofneuroprosthetics and brain-computer interfaces, that is to say directcommunication interfaces between a brain and an external device such asa computer. A brain-computer interface exploits the electricalproperties of neurons and may be designed to assist, improve or repairfaulty human action functions.

TECHNOLOGICAL BACKGROUND OF THE INVENTION

In neurobiology, a microelectrode is an element of a device making itpossible to measure a difference in electrical potential between twopoints of a biological system, for example:

-   -   between the inside of a neuron and a reference point: it is then        an intracellular microelectrode, or    -   between a point close to a neuron and a reference point: it is        then an extracellular microelectrode.

The type of signal obtained by measuring the electrical field generatedby a neuron from the interior of said neuron is very different from thatobtained by measuring said electric field from the exterior of saidneuron.

When a neuronal activity is recorded by means of an extracellularmicroelectrode, the potential difference measured reflects the currentspassing through the membrane of the neurons situated near to saidextracellular microelectrode. These membrane currents comprise:

-   -   membrane currents with rapid variations, that is to say at        frequencies of the order of 1 kHz, which underlie the creation        and the propagation of action potentials (or “spikes”), and    -   membrane currents with slower variations, that is to say at        frequencies in the interval ranging from 0 Hz to 500 Hz, called        LFP (local field potentials), which mainly underlie synaptic        activities.

By carrying out a band pass filtering of the raw signal recording thetotality of the neuronal activity, it is possible to isolate theneuronal activity corresponding uniquely to action potentials. The bandpass filtering is for example carried out between 300 Hz and 3 kHz whenthe neuronal activity linked to the action potentials is used forstudying the dynamic of sets of neurons, and for brain-computerinterface applications.

When a neuron sufficiently close to the tip of an extracellularmicroelectrode emits an action potential, the extracellularmicroelectrode records this action potential. The tip of anextracellular microelectrode being generally near to several neurons,the signal recorded by the extracellular microelectrode may comprise asuperposition of action potentials generated by several different activeneurons. A given neuron typically emits an action potential for acertain type of behavior or sensorial experience by an individual. Forexample, a first neuron of the motor cortex may emit an action potentialfor a movement of the arm towards the left whereas a second neuron ofthe motor cortex, neighboring the first neuron, emits for its part anaction potential for a movement of the arm towards the right. It is thusvery important to separate, or sort, the action potentials specific toeach neuron from the raw signal recorded by an extracellularmicroelectrode. Such a sorting of action potentials is typically carriedout by using the fact that each neuron emits on a given microelectrodeaction potentials having a specific form. The specific form, on a givenmicroelectrode, of the action potentials emitted by each neuron dependsnotably on the geometry of the neuron and the position of the neuronwith respect to the microelectrode.

In the context of brain-computer interfaces where it is sought to decodea neuronal signal to predict a behavior, such as for example a movement,better results are obtained with data of sorted action potentials thanwith data of unsorted action potentials. Even more precise results arealso obtained when the activity of a large number of neurons isrecorded. Current recording techniques make it possible to usesimultaneously hundreds of microelectrodes.

Several offline methods for sorting action potentials are known,according to which the raw signal coming from the microelectrode(s) isfirstly entirely recorded and stored before being processed. An offlinesorting method may implement long computations or resort to thesupervision of a human operator. This is not the case of a method forsorting in real time, which has to be able to process the raw signal ateach instant, progressively. FIG. 1a shows a diagram of the steps of afirst method 1 for sorting action potentials according to the prior art.The first method 1 comprises:

-   -   from input data dln, a first step st10 of detection of action        potentials and storage of waveforms of the detected action        potentials d10;    -   from the waveforms of the detected action potentials d10, a        second step st11 of extraction of relevant characteristics d11;    -   from the relevant characteristics d11, a third step st12 of        clustering said relevant characteristics d11 to obtain sorted        action potentials d12.

Different strategies may be used at each of these three steps. Duringthe first step st10, the detection of the action potentials is generallycarried out by a detection of overstepping of the amplitude or energythreshold of the raw signal. When an action potential is detected, itswaveform is recorded. The second step st11 of extraction of relevantcharacteristics aims to construct the space of the characteristics ofwaveforms before the third step st12 of clustering. Predefinedcharacteristics such as the amplitude, the width, the area, the waveletcoefficients or the complete waveform over 8 certain predefined timewindow may be used as relevant characteristics. The second step st11 mayalso comprise a sub-step of reduction of the dimensionality of the spaceof the characteristics. To do so, a conventional approach is to carryout a PCA (principal component analysis) of the matrix ofcharacteristics, such as those of waveforms. The third step st12 thenconsists in sorting the action potentials by clustering them togetherfrom the extracted and, if need be, reduced characteristics. Numerousclustering algorithms exist, among which the k-means algorithm or theexpectation-maximization algorithm. Nevertheless, these clusteringmethods generally require knowledge of the number of groups to realize.The supervision of an operator is then necessary in order to supply thisinput data.

Zhang et al. have recently proposed, in their article “A neuromorphicneural spike clustering processor for deep-brain sensing and stimulationsystems” (ISLPED, 2015), a second method 2 for sorting action potentialsby means of a network of artificial neurons implementing plasticityrules as a function of the occurrence time of the spikes, or STDP rules(spike-timing-dependent plasticity). FIG. 1b shows a diagram of thesteps of the second method 2 according to the prior art, After the firststep st10 of detection of the action potentials and recording of thewaveforms of the detected action potentials d10, the second method 2comprises a second step st20 according to which the waveforms d10 areencoded in the form of spikes d20, then a third step st21 according towhich the spikes d20 are injected into a network of artificial neuronsto obtain sorted action potentials d21. A step st22 of controlling thequality of the results obtained by the network of artificial neurons isprovided. Thanks to the STDP rules, the network of artificial neuronsthen learns to recognize the different waveforms of the actionpotentials. The first step st10 of detection of action potentials andrecording of the waveforms of the detected action potentials impliesnevertheless a preprocessing and a storage of data outside of theneuromorphical processor implementing the network of artificial neurons.

It is desired to be able to sort in real time, at each instant, theaction potentials recorded by a plurality of microelectrodes by anentirely automatic, unsupervised sorting method, and being able to beentirely implemented on a neuromorphic circuit.

SUMMARY OF THE INVENTION

The invention offers a solution to the problems evoked previously,making it possible to sort action potentials in real time and in anunsupervised manner, that is to say without return of information as afunction of the result of an output layer, in other words withoutfeedback or inverse feedback, as in the case of reinforcement learning.

One aspect of the invention relates to a method for unsupervisedsorting, in real time, of action potentials of a plurality of biologicalneurons by means of a network of artificial neurons comprising an inputlayer, an intermediate layer and an output layer, each artificial neuronof the input layer being connected to a plurality of artificial neuronsof the intermediate layer by a plurality of first excitatory synapsesand each artificial neuron of the intermediate layer being connected toa plurality of artificial neurons of the output layer by a plurality ofsecond excitatory synapses, at least one first or second excitatorysynapse connecting a first artificial neuron to a second artificialneuron and having a weight that is modified as a function of theinstants at which take place presynaptic spikes emitted by the firstartificial neuron and postsynaptic spikes emitted by the secondartificial neuron, method according to which:

-   -   the input layer receives an electrical signal measuring an        electrical activity of a plurality of biological neurons, the        electrical signal having a variable amplitude as a function of        action potentials emitted by the plurality of biological neurons        over time;    -   the input layer converts the amplitude of the electrical signal        into a train of first spikes;    -   the input layer transmits the train of first spikes to the        intermediate layer;    -   the intermediate layer converts the train of first spikes into a        train of second spikes;    -   the intermediate layer transmits the train of second spikes to        the output layer;    -   as a function of the train of second spikes, the output layer        sorts each occurrence of each type of action potential present        in the electrical signal.

The property is exploited according to which the presence of a giventype of action potential results in a given variation of amplitude inthe electrical signal.

It is thus possible to discriminate each type of action potential.Thanks to the invention, the input layer directly acquires theelectrical signal measuring the electrical activity of a plurality ofbiological neurons. By avoiding the step of detection and encoding ofthe methods of the prior art, the method for sorting action potentialsaccording to one aspect of the invention may advantageously be entirelyimplemented on a neuromorphic circuit, without requiring preprocessingand/or storage external to this neuromorphic circuit.

In the present document, “the output layer sorts each occurrence of eachtype of action potential present in the electrical signal” is taken tomean the fact that, for each type of action potential, the output layercarries out an act that is specific to said type of action potential andwhich is identical for each occurrence of said type of action potential.

Apart from the characteristics that have been evoked in the precedingparagraph, the sorting method according to one aspect of the inventionmay have one or more additional characteristics among the following,considered individually or according to all technically possiblecombinations thereof.

As a function of the train of second spikes the output layer sorts eachoccurrence of each type of action potential present in the electricalsignal by activating at the most a single group of artificial neurons ofthe output layer for each occurrence of an action potential in theelectrical signal, each group of artificial neurons of the output layercomprising at least one artificial neuron of the output layer and beingassociated with a single type of action potential and each type ofaction potential being associated with a single group of artificialneurons of the output layer. Each group of artificial neurons of theoutput layer preferentially comprises a single artificial neuron of theoutput layer. Alternatively, each group of artificial neurons of theoutput layer may comprise several artificial neurons of the outputlayer, for example in order to enable a redundancy.

The input layer is a matrix of artificial neurons having:

-   -   Na lines, the number Na of lines being chosen as a function of a        range of values in which the amplitude of the electrical signal        is variable, in such a way that the artificial neurons of a same        line are activated for a same amplitude value of the electrical        signal, and    -   Nt columns, the number Nt of columns being chosen as a function        of a time frame for observing the electrical signal, in such a        way that the artificial neurons of a same column receive the        electrical signal at a same given instant;

and at each instant t_(n)=n*dt, with n a natural integer and dt a timestep:

-   -   a first column C₀ of artificial neurons receives the electrical        signal, and    -   as a function of the amplitude value of the electrical signal        received, at least one artificial neuron of the first column C₀        emits a spike that is transmitted to the intermediate layer.

The method for sorting action potentials according to one aspect of theinvention carries out a storage of information uniquely over a durationcorresponding to the time frame for observing the electrical signal. Thetime frame for observing the electrical signal is typically of the orderof the duration of an action potential.

The time frame for observing the electrical signal is thus generallycomprised between 0.1 ms and 5 ms, and preferentially comprised between0.5 ms and 1 ms.

A margin is defined around each amplitude value of the electrical signalreceived in such a way that, at each instant t_(n)=n*dt:

-   -   the first column C₀ of artificial neurons receives the        electrical signal, and    -   as a function of the amplitude value of the electrical signal        received and of the margin defined around said amplitude value,        at least two artificial neurons of the first column C₀ each emit        a spike, each spike being transmitted to the intermediate layer.

Thanks to this margin, advantageously a sensitivity interval is definedfor each artificial neuron of the input layer. The union of thesensitivity intervals of all the artificial neurons of the input layertypically covers the range of values in which the amplitude of thesignal is variable. There exists an overlap between the sensitivityintervals in such a way that for each given amplitude value of theelectrical signal received, several artificial neurons of the inputlayer react by each emitting a spike. In this way, the robustness of themethod according to one aspect of the invention is increased.

The number Nt of columns of the input layer being strictly greater than1, at each instant t_(k)=t_(n)+k*dt′ and for each column C_(k) ofartificial neurons, with dt′ a second time step and k a natural integersuch that 1≤k≤Nt−1, each artificial neuron of same line as an artificialneuron of the first column C₀ having emitted a spike at the instantt_(n), emits in its turn a spike that is transmitted to the intermediatelayer.

This makes it possible that the electrical signal is received uniquelyby the artificial neurons of the first column C₀, and not necessarily byall of the artificial neurons of the input layer. The information ofamplitude variation of the electrical signal, initially received by thefirst column C₀ of artificial neurons, may be transmitted little bylittle to the other columns of artificial neurons of the input layer.Alternatively, the first column C₀ of artificial neurons transformingthe information of amplitude variation of the electrical signal that itreceives into a spike emission information by one or more lines ofartificial neurons, this spike emission information may be transmittedlittle by little to the other columns of the input layer. The secondtime step dt′ may be identical to the time step dt or distinct from thetime step dt.

Each artificial neuron of the input layer is connected to a plurality ofartificial neurons of the intermediate layer by a plurality of firstexcitatory synapses in such a way that a spike emitted by saidartificial neuron of the input layer is transmitted to the plurality ofartificial neurons of the intermediate layer by the plurality of firstexcitatory synapses.

Each artificial neuron of the intermediate layer is connected to aplurality of artificial neurons of the output layer by a plurality ofsecond excitatory synapses in such a way that a spike emitted by saidartificial neuron of the intermediate layer is transmitted to theplurality of artificial neurons of the output layer by the plurality ofsecond excitatory synapses. Each excitatory synapse has a weight, eachartificial neuron of the intermediate layer and each artificial neuronof the output layer have a potential having initially a value designated“rest value”.

When an excitatory synapse transmits a spike to an artificial neuron ofthe intermediate layer or of the output layer, the potential of saidartificial neuron increases proportionally to the weight of said firstexcitatory synapse. When the potential of an artificial neuron of theintermediate layer or of the output layer exceeds a threshold value,said artificial neuron emits a spike and its potential is lowered to areset value or alternatively said artificial neuron is prevented fromre-emitting a spike for a refractory period. In the absence of spike atthe input of an artificial neuron of the intermediate layer or of theoutput layer and when this neuron does not itself emit a spike, thepotential of said neuron returns to its rest value in a characteristictime T_(m).

This mechanism makes it possible to avoid the artificial neurons fromemitting spikes in a non-specific manner.

The manner in which the potential of each artificial neuron increases orreturns to its rest value is typically determined by a LIF(leaky-integrate-and-fire) model. The weight of a synapse is also called“synaptic weight”. The potential of an artificial neuron is also called“membrane potential” or “transmembrane potential”.

The weight of each excitatory synapse is modified as a function of apredefined time window:

-   -   for a given excitatory synapse, when the predefined time window        comprises a presynaptic spike and a postsynaptic spike, the        weight of this excitatory synapse is increased;    -   for a given excitatory synapse, when the predefined time window        comprises a postsynaptic spike only, the weight of this        excitatory synapse is decreased;    -   for a given excitatory synapse, when the predefined time window        comprises a presynaptic spike only, the weight of this        excitatory synapse remains unchanged.

For a given excitatory synapse connecting a first artificial neuron to asecond artificial neuron, “presynaptic spike” is taken to mean a spikeemitted by the first artificial neuron and transmitted by saidexcitatory synapse to the second artificial neuron and “postsynapticspike” is taken to mean a spike emitted by the second artificial neuron.

This mechanism contributes to the learning, by the network of artificialneurons, of each waveform of action potential.

Each artificial neuron of the input layer is connected to a plurality ofartificial neurons of the intermediate layer by a plurality of firstexcitatory synapses in such a way that a spike emitted by an artificialneuron of the input layer is transmitted to the plurality of artificialneurons of the intermediate layer. For a first given excitatory synapseconnecting an artificial neuron of the input layer to an artificialneuron of the intermediate layer, “presynaptic artificial neuron” istaken to mean the artificial neuron of the input layer and “postsynapticartificial neuron” is taken to mean the artificial neuron of theintermediate layer.

According to a first embodiment, each first excitatory synapse has aweight allotted a synaptic coefficient P_(rel) such that 0≤P_(rel)≤1,the synaptic coefficient P_(rel) decreasing when the presynapticartificial neuron emits a spike, and the synaptic coefficient P_(rel)increasing towards 1 otherwise with a characteristic time T_(stp). Eachpostsynaptic artificial neuron receiving a spike via a first excitatorysynapse is excited proportionally to the product of the synapticcoefficient P_(rel) and the weight of said first excitatory synapse.This characteristic, designated “short term plasticity” between theinput layer and the intermediate layer, advantageously makes it possibleto contribute to filtering the noise of the electrical signal receivedby the input layer in order that the artificial neurons of theintermediate layer are not activated by the noise, and thus that theartificial neurons of the output layer are not activated by the noise.

Alternatively to the characteristic of short term plasticity between theinput layer and the intermediate layer according to the firstembodiment, a characteristic short term plasticity between theintermediate layer and the output layer may be provided in order thatthe artificial neurons of the output layer are not activated by noise.Each artificial neuron of the intermediate layer is connected to aplurality of artificial neurons of the output layer by a plurality ofsecond excitatory synapses in such a way that a spike emitted by anartificial neuron of the intermediate layer is transmitted to theplurality of artificial neurons of the output layer. For a second givenexcitatory synapse connecting an artificial neuron of the intermediatelayer to an artificial neuron of the output layer, “presynapticartificial neuron” is taken to mean the artificial neuron of theintermediate layer and “postsynaptic artificial neuron” is taken to meanthe artificial neuron of the output layer. Each second excitatorysynapse has a weight allotted a synaptic coefficient P_(rel) such that0≤P_(rel)≤1, the synaptic coefficient P_(rel) decreasing when thepresynaptic artificial neuron emits a spike, and the synapticcoefficient P_(rel) increasing towards 1 otherwise with a characteristictime T_(stp). Each postsynaptic artificial neuron receiving a spike viaa second excitatory synapse is excited proportionally to the product ofthe synaptic coefficient P_(rel) and the weight of said secondexcitatory synapse.

It is possible to provide both the characteristic of short termplasticity between the input layer and the intermediate layer, and thecharacteristic of short term plasticity between the intermediate layerand the output layer.

According to a second embodiment, the network of artificial neurons alsocomprises at least one artificial detection neuron, each artificialneuron of the input layer being connected to the artificial detectionneuron by a first excitatory detection synapse, and the artificialdetection neuron being connected to a plurality of artificial neurons ofthe intermediate layer by a plurality of second excitatory detectionsynapses. According to the second embodiment, each first excitatorydetection synapse has a weight allotted a synaptic coefficient P_(rel)such that 0≤P_(rel)≤1, the synaptic coefficient P_(rel), decreasing whenthe presynaptic artificial neuron emits a spike and the synapticcoefficient P_(rel) increasing towards 1 otherwise with a characteristictime T_(stp), and the artificial detection neuron receiving a spike viaa first excitatory detection synapse is excited proportionally to theproduct of the synaptic coefficient P_(rel) and the weight of said firstexcitatory detection synapse. According to the second embodiment, ashort term plasticity rule is thus implemented uniquely between theartificial neurons of the input layer and the artificial detectionneuron, and not between the artificial neurons of the input layer andthe artificial neurons of the intermediate layer. The binary detectionfunction is thus separated, that is to say “presence” or “absence”, fromthe action potentials on the one hand, and the discrimination functionof the action potentials present on the other hand: the artificialdetection neuron ensures the binary detection function thanks to theshort term plasticity rule whereas the artificial neurons of theintermediate layer ensure the discrimination function thanks to a STDPrule. The artificial detection neuron emits spikes when it detects thepresence of an action potential in the train of first spikes emitted bythe artificial neurons of the input layer and transmitted via the firstexcitatory detection synapses, and do not emit a spike otherwise. Thespikes emitted by the artificial detection neuron are transmitted to theartificial neurons of the intermediate layer via the second excitatorydetection synapses. Thus, as a function of the spikes that it emits, theartificial detection neuron modulates the activity of the artificialneurons of the intermediate layer.

According to an improvement of the second embodiment, the network ofartificial neurons comprises a recurrent excitatory synapse, from theartificial detection neuron towards itself. Thus, once the spikeemission threshold of the artificial detection neuron is overstepped,the artificial detection neuron receives an additional excitation by therecurrent excitatory synapse. The excitation coming from the artificialneurons of the input layer thus has to descend below a threshold lessthan the preceding emission threshold in order that the artificialdetection neuron ceases to emit spikes, according to a hysteresismechanism. This makes it possible to ensure a continuity in thedetection, even in the case where the form of the action potentialprovisionally passes by values close to zero. The detection function isthus improved.

According to an improvement of the first or the second embodiment, anartificial neuron of the intermediate layer or of the output layer mayreceive a spike of an artificial neuron of the preceding layer both viaan excitatory synapse and via an inhibitory synapse, each synapseobeying an STDP rule. The STDP rule of the excitatory synapse isreversed with respect to the STDP rule of the inhibitory synapse, insuch a way that when the weight of the excitatory synapse increases,that of the inhibitory synapse decreases, and conversely when the weightof the excitatory synapse decreases, that of the inhibitory synapseincreases. Thus, the sum of the weights of the excitatory synapse and ofthe inhibitory synapse is not cancelled out—except if each of the twoweights is zero, because when the weight of the excitatory synapse ishigh, that of the inhibitory synapse is low and vice versa. Usingnegative contributions through inhibitory synapses in addition to thepositive contributions of the excitatory synapses makes it possible toimprove the recognition of the different patterns of action potentials.

According to another improvement of the first or the second embodiment,an artificial neuron of the intermediate layer or of the output layermay receive a same spike of an artificial neuron of the preceding layervia a plurality of excitatory synapses each having a differenttransmission delay and/or via a plurality of inhibitory synapses eachhaving a different transmission delay, each synapse obeying a STDP law.For example, an artificial neuron may thus receive simultaneously:

-   -   a spike coming from a first artificial neuron of the preceding        layer via a synapse having a short delay, and    -   a spike coming from a second artificial neuron of the preceding        layer via a synapse having a long delay.

In this example, there is then an information on the fact that thesecond artificial neuron has emitted a spike before the first artificialneuron. Generally speaking, this improvement enables a layer ofartificial neurons to have an information on the relative instants ofemission of a spike by the artificial neurons of the preceding layer.The precision of the sorting method according to one aspect of theinvention is thus improved, enabling it to differentiate a larger numberof patterns.

According to an improvement of the second embodiment, the artificialdetection neuron is connected to a plurality of artificial neurons ofthe output layer by a plurality of second inhibitory detection synapses:the spikes of the artificial detection neuron, transmitted to theartificial neurons of the output layer via the plurality of secondinhibitory detection synapses, force the artificial neurons of theoutput layer to reach the end of an action potential before emitting aspike. This thus contributes to controlling the instant of emission of aspike by the artificial neurons of the output layer. In particular, thiscontributes to avoiding that an artificial neuron of the output layeremits a spike before the end of an action potential present in thesignal. In fact, if an artificial neuron of the output layer emits aspike before the end of an action potential, it risks missing importantinformation to sort the action potential in question, as is for examplethe case when two types of action potentials begin in the same way butfinish differently. According to this improvement, the artificialneurons of the output layer are inhibited by the artificial detectionneuron throughout the duration of an action potential. It is thusensured that the output artificial neurons can be excited after the endof the action potential, for example by introducing a transmission delayin the synaptic connections between the intermediate layer and theoutput layer. In fact, since the artificial neurons of the output layerare inhibited for the duration of an action potential, whereas theartificial neurons of the intermediate layer only emit spikes for theduration of an action potential, if it is not ensured that theartificial neurons of the output layer can be excited after the end ofthe action potential, they will not a priori ever be excited.

Each artificial neuron of the intermediate layer is connected to all ofthe other artificial neurons of the intermediate layer by a plurality offirst inhibitory synapses in such a way that a spike emitted by saidartificial neuron of the intermediate layer is transmitted to all of theother artificial neurons of the intermediate layer by the plurality offirst inhibitory synapses. Each artificial neuron of the output layer isconnected to all of the other artificial neurons of the output layer bya plurality of second inhibitory synapses in such a way that a spikeemitted by said artificial neuron of the output layer is transmitted toall of the other artificial neurons of the output layer by the pluralityof second inhibitory synapses. According to a first alternative, when aninhibitory synapse transmits a spike to an artificial neuron of theintermediate layer or of the output layer, said artificial neuron isprevented from emitting a spike for a predefined duration designated“inhibition period”. According to a second alternative, when aninhibitory synapse transmits a spike to an artificial neuron of theintermediate layer or of the output layer, the potential of saidartificial neuron is decreased proportionally to the weight of saidinhibitory synapse. The use of an inhibition period, in the firstalternative, makes it possible to manage the time between two successivespikes more precisely than in the second alternative. The reduction inpotential used in the second alternative enables greater flexibility:for example, if two action potentials arrive simultaneously or nearlysimultaneously, the output layer could emit two spikes corresponding tothese action potentials despite the inhibition. According to a thirdalternative combining the first and second alternatives, when aninhibitory synapse transmits a spike to an artificial neuron of theintermediate layer or of the output layer, said artificial neuron isprevented from emitting a spike for a predefined duration designated“inhibition period” and the potential of said artificial neuron isdecreased proportionally to the weight of said inhibitory synapse.

This “winner takes all” type mechanism advantageously contributes topreventing several artificial neurons from learning the same actionpotential waveform. In the case where the output layer activates, foreach occurrence of an action potential in the electrical signal, asingle group of artificial neurons of the output layer comprisingseveral artificial neurons of the output layer, there is advantageouslyno lateral inhibition between the artificial neurons of a same group.

A plurality of second excitatory synapses connects each artificialneuron of the intermediate layer to a plurality of artificial neurons ofthe output layer, each second excitatory synapse having a weight. Foreach second excitatory synapse, when an artificial neuron of the outputlayer receives, in a predefined time window, a spike transmitted by saidsecond excitatory synapse and a spike transmitted by a second inhibitorysynapse, then the weight of said second excitatory synapse is decreased.For each second excitatory synapse, when an artificial neuron of theoutput layer receives, in the predefined time window, a spiketransmitted by said second excitatory synapse and no spike transmittedby a second inhibitory synapse, then the weight of said secondexcitatory synapse is increased.

This mechanism, herein called inhibition induced plasticity,advantageously contributes to preventing several artificial neurons fromlearning the same action potential waveform and thus increases learningprecision. The inhibition induced plasticity mechanism is advantageouslycombined with the “winner takes all” type mechanism describedpreviously.

Each artificial neuron of the output layer has a potential; eachartificial neuron of the output layer emits a spike when its potentialexceeds a threshold value. The threshold value of each artificial neuronof the output layer emitting a spike at an instant t is increasedproportionally to the number of spikes received by said artificialneuron in a time window around the instant t. The threshold value Th ofeach artificial neuron of the output layer emitting a spike at aninstant t1 is decreased in such a way that:Th(t2)=α*Th(t1)

with Th(t1) the threshold value at the instant t1, Th(t2) the thresholdvalue at an instant t2 later than t1 and α a real number such that0<α<1.

The above mechanism introduces a plasticity on the threshold value ofeach artificial neuron of the output layer, called intrinsic plasticity.Advantageously the robustness of the method according to one aspect ofthe invention to potential variations, from one waveform to another, ofthe number of spikes transmitted to the output layer is thus increased.During an initialization period, or learning period, of the method forsorting action potentials according to one aspect of the invention, andalthough a mechanism of “winner takes all” type is implemented, it mayhappen that several artificial neurons of the output layer emit, oneafter the other, spikes for a same action potential if their thresholdis poorly suited. The intrinsic plasticity mechanism that has beendescribed has the advantage of not depending on the precise instant t ofemission of each spike by an artificial neuron of the output layer,thanks to the time window that surrounds the instant t. This makes itpossible to improve learning by contributing to guaranteeing that anaction potential activates a single group of neurons of the outputlayer.

Alternatively, another intrinsic plasticity mechanism may be used. Thethreshold value of each artificial neuron of the output layer emitting aspike at an instant t is decreased proportionally to the number ofspikes received by said artificial neuron in a first time window beforethe instant t. The threshold value of each artificial neuron of theoutput layer emitting a spike at an instant t is increasedproportionally to the number of spikes received by said artificialneuron in a second time window after the instant t.

The above alternative mechanism also advantageously introduces aplasticity on the threshold value of each artificial neuron of theoutput layer in order to increase the robustness of the method accordingto one aspect of the invention to potential variations, from onewaveform to another, of the number of spikes transmitted to the outputlayer.

When an intrinsic plasticity is introduced on the threshold value ofeach artificial neuron of the output layer, according to one or theother of the two alternatives that have been described, preferentially,the “winner takes all” type mechanism and the mechanism of inhibitioninduced plasticity between the intermediate layer and the output layerare also implemented. This thus contributes to guaranteeing that a givenaction potential is only learnt by a single artificial neuron of theoutput layer, despite the variability introduced on the threshold valueof each artificial neuron of the output layer.

The network of artificial neurons comprises the input layer, theintermediate layer, a second intermediate layer and the output layer,and:

-   -   the input layer transmits the train of first spikes to the        intermediate layer and to the second intermediate layer;    -   the second intermediate layer converts the train of first spikes        into a second train of second spikes;    -   the second intermediate layer transmits the second train of        second spikes to the output layer;    -   as a function of the train of second spikes and the second train        of second spikes, the output layer sorts each occurrence of each        type of action potential present in the electrical signal.

In this configuration, a double processing of the train of first spikesis carried out in parallel by the first and second intermediate layers.

This configuration advantageously makes it possible to increase therobustness of the method according to one aspect of the invention. Theweight of each excitatory synapse connecting an artificial neuron of theinput layer to an artificial neuron of the intermediate layer or to anartificial neuron of the second intermediate layer is typicallyinitialized randomly. Consequently, the train of second spikes at theoutput of the intermediate layer is a priori different from the secondtrain of second spikes at the output of the second intermediate layer.Each intermediate layer is thus likely to have, in certain cases, lessgood results than the other. It is on the other hand not very probablethat two different intermediate layers commit the same errors. Which iswhy combining two intermediate layers makes it possible to increase theperformances.

The network of artificial neurons comprises the input layer, theintermediate layer, a second intermediate layer and the output layer,and:

-   -   a part of the input layer transmits a second train of first        spikes to the second intermediate layer;    -   the second intermediate layer converts the second train of first        spikes into a second train of second spikes;    -   the second intermediate layer transmits the second train of        second spikes to the output layer;    -   as a function of the train of second spikes and the second train        of second spikes, the output layer sorts each occurrence of each        type of action potential present in the electrical signal.

In this configuration, the input layer transmits the train of firstspikes to the intermediate layer whereas the part of the input layertransmits the second train of first spikes to the second intermediatelayer: the second train of first spikes is a part of the train of firstspikes. In other words, the second train of first spikes is included inthe train of first spikes.

The input layer being a matrix of artificial neurons, the part of theinput layer may comprise the same number of lines as the input layer anda number of columns less than that of the input layer. In this case, thepart of the input layer makes it possible to take specifically intoaccount a small time frame for observing the electrical signal withinthe time frame for observing the input layer. The choice of the size ofthe observation time frame has an influence on the results obtained. Thelarger the observation time frame, the less errors due to noise aresuffered. However, a too large observation time frame, that is to saytypically an observation time frame larger than the duration of anaction potential, contains a lot of insignificant signal and does notmake it possible to obtain a relevant result.

Choosing several observation time frames of different sizes thus makesit possible to make the best of each size, without knowing precisely theideal size of an observation time frame—which is not necessarily thesame for the different action potentials. Alternatively, the part of theinput layer may comprise the same number of columns as the input layerand a number of lines less than that of the input layer.

Alternatively, the network of artificial neurons comprises the inputlayer, a second input layer, the intermediate layer and the outputlayer, and:

-   -   the second input layer receives a second electrical signal        measuring an electrical activity of a second plurality of        biological neurons, the second electrical signal having a        variable amplitude as a function of action potentials emitted by        the second plurality of biological neurons over time;    -   the second input layer converts the amplitude of the second        electrical signal into a second train of first spikes;    -   the second input layer transmits the second train of first        spikes to the intermediate layer;    -   the intermediate layer converts the train of first spikes and        the second train of first spikes into a train of second spikes.

The second electrical signal may be different from the first electricalsignal or identical to the first electrical signal. When the secondelectrical signal is different from the first electrical signal, thesecond electrical signal may for example be the derivative of the firstelectrical signal, or the first and second electrical signals may comefrom two distinct extracellular microelectrodes. This configuration hasa particular interest when several extracellular microelectrodes closeto each other are used to record the electrical activity of the samebiological neurons. The first electrical signal is for example recordedby a first extracellular microelectrode and the second electrical signalis for example recorded by a second extracellular microelectrode near tothe first extracellular electrode; the first and second extracellularmicroelectrodes recording the electrical activity of common biologicalneurons.

The artificial neurons of the input layer having a certain sensitivityinterval, the artificial neurons of the second input layeradvantageously have another sensitivity interval, distinct from thesensitivity interval of the artificial neurons of the input layer. Infact, each sensitivity interval is preferentially chosen as a functionof the noise level.

In particular, each sensitivity interval is preferentially chosensubstantially equal to three times the noise level. But this assumesknowing a priori the noise level.

The network of artificial neurons comprises the input layer, a secondinput layer, the intermediate layer, a second intermediate layer and theoutput layer, and:

-   -   the second input layer receives a second electrical signal        measuring an electrical activity of a second plurality of        biological neurons, the second electrical signal having a        variable amplitude as a function of action potentials emitted by        the second plurality of biological neurons over time;    -   the second input layer converts the amplitude of the second        electrical signal into a second train of first spikes;    -   the second input layer transmits the second train of first        spikes to the second intermediate layer;    -   the second intermediate layer converts the second train of first        spikes into a second train of second spikes;    -   the second intermediate layer transmits the second train of        second spikes so to the output layer;    -   as a function of the train of second spikes and the second train        of second spikes, the output layer sorts each occurrence of each        type of action potential present in the electrical signal.

The second electrical signal may be different from the first electricalsignal or identical to the first electrical signal.

Compared to the preceding configuration where several input layers areconnected to a single intermediate layer, this configuration accordingto which each input layer is connected to its own intermediate layeradvantageously makes it possible that each intermediate layer has lesspatterns, or waveforms, to learn: the robustness and the performances ofthe network of artificial neurons are thus increased.

Another aspect of the invention relates to a network of artificialneurons for the implementation of a method for unsupervised sorting, inreal time, of action potentials of a plurality of biological neurons,the network of artificial neurons comprising:

-   -   an input layer for the reception of an electrical signal having        a variable amplitude as a function of action potentials emitted        by the plurality of biological neurons over time, the conversion        of the electrical signal into a train of first spikes and the        transmission of the train of first spikes to an intermediate        layer;    -   said intermediate layer for the conversion of the train of first        spikes into a train of second spikes and the transmission of the        train of second spikes to an output layer;    -   said output layer for the sorting, as a function of the train of        second spikes, of each occurrence of each type of action        potential present in the electrical signal;

each artificial neuron of the input layer being connected to a pluralityof artificial neurons of the intermediate layer by a plurality of firstexcitatory synapses and each artificial neuron of the intermediate layerbeing connected to a plurality of artificial neurons of the output layerby a plurality of second excitatory synapses, each first or secondexcitatory synapse connecting a first artificial neuron to a secondartificial neuron and having a weight that is modified as a function ofthe instants at which take place presynaptic spikes emitted by the firstartificial neuron and postsynaptic spikes emitted by the secondartificial neuron.

The invention and its different applications will be better understoodon reading the description that follows and by examining the figuresthat accompany it.

BRIEF DESCRIPTION OF THE FIGURES

The figures are presented for indicative purposes and in no way limitthe invention.

FIG. 1a shows a diagram of the steps of a first method for supervisedand offline sorting of action potentials according to the prior art.

FIG. 1b shows a diagram of the steps of a second method for offlinesorting of action potentials according to the prior art.

FIG. 2a shows a diagram of the steps of a method according to one aspectof the invention for unsupervised sorting, in real time, of actionpotentials of a plurality of biological neurons by means of a network ofartificial neurons.

FIG. 2b schematically shows a first network of artificial neuronsaccording to a first embodiment for the implementation of the method ofFIG. 2a , the first network of artificial neurons according to the firstembodiment comprising an input layer, an intermediate layer and anoutput layer.

FIG. 2c schematically shows a first network of artificial neuronsaccording to a second embodiment for the implementation of the method ofFIG. 2a , the first network of artificial neurons according to thesecond embodiment further comprising an artificial detection neuron.

FIG. 3a schematically shows the input layer of the first network ofartificial neurons of FIG. 2b receiving an electrical signal andconverting the amplitude of the electrical signal into a train of firstspikes.

FIG. 3b schematically illustrates the definition of a margin around anamplitude value to obtain a sensitivity interval of an artificial neuronof the input layer of the first network of artificial neurons of FIG. 2b.

FIG. 3c schematically shows an overlap of the sensitivity intervals ofthe artificial neurons of the input layer of the first network ofartificial neurons of FIG. 2 b.

FIG. 4a schematically shows a plurality of first inhibitory synapsesinterconnecting the artificial neurons of the intermediate layer of thefirst network of artificial neurons of FIG. 2 b.

FIG. 4b schematically shows a plurality of second inhibitory synapsesinterconnecting the artificial neurons of the output layer of the firstnetwork of artificial neurons of FIG. 2 b.

FIG. 5 schematically shows a second network of artificial neurons forthe implementation of the method of FIG. 2 a.

FIG. 6 schematically shows a third network of artificial neurons for theimplementation of the method of FIG. 2 a.

FIG. 7 schematically shows a fourth network of artificial neurons forthe implementation of the method of FIG. 2 a.

FIG. 8 schematically shows a fifth network of artificial neurons for theimplementation of the method of FIG. 2 a.

DETAILED DESCRIPTION OF AT LEAST ONE EMBODIMENT OF THE INVENTION

Unless stated otherwise, a same element appearing in the differentfigures has a single reference.

In the present application, the terms “synapse” and “artificial synapse”are employed indiscriminately. In the case of a synapse connecting afirst artificial neuron to a second artificial neuron:

-   -   the first artificial neuron is also called “presynaptic neuron”,        vis-à-vis said synapse, and    -   the second artificial neuron is also called “postsynaptic        neuron”, vis-à-vis said synapse.

When the first neuron emits a spike that is transmitted to the secondartificial neuron, this spike is also called “presynaptic spike”,vis-à-vis the second artificial neuron. When the second artificialneuron emits a spike, this spike is also called “postsynaptic spike”,vis-à-vis the second artificial neuron.

FIGS. 1a and 1b have been described in the technological background ofthe invention.

FIG. 2a shows a diagram of the steps of a method 100 according to oneaspect of the invention for unsupervised sorting, in real time, ofaction potentials of a plurality of biological neurons by means of anetwork of artificial neurons. FIG. 2b schematically shows a firstnetwork of artificial neurons 10 according to a first embodiment, forthe implementation of the method 100. FIG. 2c schematically shows afirst network of artificial neurons 10′ according to a secondembodiment, for the implementation of the method 100.

FIGS. 2a, 2b and 2c are described jointly.

The first network of artificial neurons 10, 10′ according to the firstor the second embodiment comprises:

-   -   an input layer 11 comprising a plurality of artificial neurons        n11,    -   an intermediate layer 13 comprising a plurality of artificial        neurons n13, and    -   an output layer 15 comprising a plurality of artificial neurons        n15.

According to an embodiment, designated “all-to-all”, a plurality offirst excitatory synapses set connects each artificial neuron of theinput layer n11 to the plurality of artificial neurons of theintermediate layer n13. A plurality of second excitatory synapses se2connects each artificial neuron of the intermediate layer n13 to theplurality of artificial neurons of the output layer n15. In other words:

-   -   each artificial neuron of the intermediate layer n13 receives a        first excitatory synapse se1 coming from each artificial neuron        of the input layer n11, and    -   each artificial neuron of the intermediate layer n13 sends a        second excitatory synapse se2 to each artificial neuron of the        output layer n15.

Alternatively to an “all-to-all” connection between the artificialneurons n11 of the input layer and the artificial neurons n13 of theintermediate layer on the one hand, and between the artificial neuronsn13 of the intermediate layer and the artificial neurons n15 of theoutput layer on the other hand, one or more partial connections may beenvisaged. For example, one or more artificial neurons n11 of the inputlayer may only be connected to a part of the artificial neurons n13 ofthe intermediate layer. Similarly, one or more artificial neurons n13 ofthe intermediate layer may only be connected to a part of the artificialneurons n15 of the output layer.

According to the embodiment generally described in the presentapplication, all the excitatory synapses of the first network ofartificial neurons go in the same direction (feedforward excitation), tobe specific: from the input layer 11 to the output layer 15. A networkof artificial neurons, designated “recurrent”, may alternatively be usedin which certain excitatory synapses go backwards, from the output layerto the input layer.

The first network of artificial neurons 10′ according to the secondembodiment, illustrated in FIG. 2c , further comprises an artificialdetection neuron nD. For the sake of clarity, the first and secondexcitatory synapses se1, se2 are not represented in FIG. 2c . Eachartificial neuron n11 of the input layer is connected to the artificialdetection neuron nD via a first excitatory detection synapse se1D, andthe artificial detection neuron nD is connected to each artificialneuron n13 of the intermediate layer via a plurality of secondexcitatory detection synapses se2D. Alternatively, only a part of theartificial neurons n11 of the input layer could be connected to theartificial detection neuron nD, and/or the artificial detection neuronnD could just be connected to a part only of the artificial neurons n13of the intermediate layer.

According to an improvement of the first network of artificial neurons10′ according to the second embodiment, the artificial detection neuronnD is connected to each artificial neuron n15 of the output layer by asecond inhibitory detection synapse si2D.

According to step 111 of the method 100 for unsupervised sorting, inreal time, of action potentials of a plurality of biological neurons,the input layer 11 receives an electrical signal dln. The electricalsignal dln measures an electrical activity of a plurality of biologicalneurons and has a variable amplitude as a function of action potentialsemitted by the plurality of biological neurons over time.

According to step 112 of the method 100, the input layer 11 nextconverts the amplitude of the electrical signal dln into a train offirst spikes. The train of first spikes comprises all the spikes thatare emitted by the artificial neurons of the input layer n11.

After step 112, the method 100 comprises a step 113 according to whichthe input layer 11 transmits the train of first spikes to theintermediate layer 13 via the plurality of first excitatory synapsesse1.

The intermediate layer 13 then converts the train of first spikes into atrain of second spikes, according to step 131 of the method 100, thenthe train of second spikes is transmitted to the output layer 15 via theplurality of second excitatory synapses se2 during a step 132 of themethod 100. The train of second spikes comprises all the spikes that areemitted by the artificial neurons of the intermediate layer n13.

Finally, in step 151 of the method 100, the output layer 15 sorts eachoccurrence of each type of action potential present in the electricalsignal dln, as a function of the train of second spikes by activating atthe most a single group of artificial neurons of the output layer n15for each occurrence of an action potential in the electrical signal dln,each group of artificial neurons of the output layer n15 beingassociated with a single type of action potential and each type ofaction potential being associated with a single group of artificialneurons of the output layer. A group of artificial neurons may compriseseveral artificial neurons or instead, preferentially, a singleartificial neuron.

FIG. 3a schematically shows the input layer 11 when it receives theelectrical signal dln then converts the amplitude of the electricalsignal dln into a train of first spikes. FIG. 3b schematicallyillustrates the definition of a margin Mar around an amplitude value Vato obtain a sensitivity interval Sen of an artificial neuron of theinput layer n11. FIG. 3c schematically shows an overlap of thesensitivity intervals Sen of the artificial neurons of the input layern11. FIGS. 3a, 3b and 3c are described jointly.

The input layer 11 is typically a matrix of artificial neurons n11comprising Na lines and Nt columns. The number Nt of columns istypically chosen as a function of a time frame for observing theelectrical signal dln, in such a way that the artificial neurons n11 ofa same column receive the electrical signal at a same given instant.

The number Na of lines is typically chosen as a function of a range ofvalues in which the amplitude of the electrical signal is variable, insuch a way that:

-   -   the artificial neurons n11 of a same line are activated for a        same amplitude value of the electrical signal dln, and    -   the artificial neurons of distinct lines are activated for        distinct amplitude values Va of the electrical signal dln.

Each artificial neuron n11 of a same column is thus associated with adistinct amplitude value Va of the electrical signal dln in such a waythat all of the artificial neurons n11 of a same column scan the rangeof values in which the amplitude of the electrical signal dln isvariable.

At each instant t_(n)=n*dt, with n a natural integer and dt a time step,a first column C₀ of artificial neurons n11 receives the electricalsignal dln and as a function of the amplitude value of the electricalsignal dln received, at least one artificial neuron n11 of the firstcolumn C₀ emits a spike that is transmitted to the intermediate layer13. In FIG. 3a , an artificial neuron emitting a spike is referenced11_1 and represented by a full circle whereas an artificial neuron notemitting a spike is referenced 11_0 and represented by an empty circle.

A margin Mar is preferentially defined around each amplitude value Va ofthe electrical signal dln received in such a way that each artificialneuron of the input layer n11 has a sensitivity interval Sen. Thus, anartificial neuron of the input layer n11 emits a spike when theamplitude value Va of the electrical signal dln is in the sensitivityinterval of said artificial neuron n11. The number Na of lines and thesize of the sensitivity intervals Sen are preferentially chosen as afunction of the range of values in which the amplitude of the electricalsignal is variable in such a way that:

-   -   all of the sensitivity intervals Sen scan the range of values in        which the amplitude of the electrical signal dln is variable,        and    -   the artificial neurons n11 of consecutive lines have their        sensitivity intervals Sen that overlap.

Thanks to the sensitivity intervals Sen and their overlap, at eachinstant t_(n)=n*dt:

-   -   the first column C₀ of artificial neurons n11 receives a sample        of the electrical signal dln, and    -   at least two artificial neurons n11 of the first column C₀ each        emit a spike, each spike being transmitted to the intermediate        layer 13.

In the particular example of FIG. 3c , the margin Mar around eachamplitude value Va is chosen equal to 1.5 times the noise level and thewidth of the sensitivity interval Sen is thus equal to 3 times the noiselevel. This choice ensures a probability distribution of the spikesenabling good learning. The overlap of the sensitivity intervals Sen isnext configured in order that eight artificial neurons n11 of the firstcolumn C₀ emit a spike at each instant t_(n).

The number Nt of columns being strictly greater than 1, at each instantt_(k)=t_(n)+k*dt′ and for each column C_(k) of artificial neurons n11,with dt′ a second time step and k a natural integer such that1≤k<(Nt−1), each artificial neuron n11 of same line as an artificialneuron n11 of the first column C₀ having emitted a spike at the instanttn, emits in its turn a spike that is transmitted to the intermediatelayer 13. The number Nt of columns is preferentially chosen such thatthe time frame for observing the electrical signal dln is slightly lessthan the minimum duration of an action potential. In an exemplaryembodiment, the time frame for observing the electrical signal dln ischosen equal to 0.9 ms. In an exemplary embodiment, the second time stepdt′ is equal to the time step dt.

In the embodiment that has been described until now, each artificialneuron n11 of the input layer is sensitive to an amplitude value at agiven instant. Alternatively, each artificial neuron n11 of the inputlayer may be sensitive to the amplitude values in a given timesensitivity window. In this case, an artificial neuron n11 of the inputlayer emits a spike if at least one of the amplitude values receivedduring its sensitivity time window is in its sensitivity interval. Thisalternative embodiment may bring greater robustness to the method 100according to one aspect of the invention, particularly when theelectrical signal associated with an action potential comprises rapidamplitude variations, which has the consequence that the amplitudevalues sampled strongly depend on the synchronization between saidaction potential and the sampling.

The behavior of the artificial neurons of the intermediate layer n13 andthe artificial neurons of the output layer n15 is typically defined byan LIF (Leaky-Integrate-and-Fire) model. According to this LIF model,each artificial neuron has a potential, also called membrane potentialor transmembrane potential, and each synapse has a weight, also calledsynaptic weight. Each time that an artificial neuron receives a spikevia a synapse, the potential of this artificial neuron is modifiedproportionally to the weight of this synapse. In the case of anexcitatory synapse, the potential of the artificial neuron is increasedproportionally to the weight of this synapse; in the case of aninhibitory synapse, the potential of the artificial neuron is decreasedproportionally to the weight of this synapse.

When the potential of an artificial neuron reaches a certain thresholdvalue Th, the artificial neuron emits a spike and its potential isbrought back to a reset value V_(RESET). The reset value V_(RESET) isnotably chosen as a function of the threshold value: the objective isthat the value of the potential of an artificial neuron having emitted aspike is brought back to a value close to the value of the restpotential, or less than the value of the rest potential.

According to the LIF model, the value of the potential of eachartificial neuron respects the following equation:

$\frac{dV}{dt} = {{{- \frac{1}{\tau_{m}}} \cdot {V(t)}} + {\sum\limits_{t}{\sum\limits_{s}{{w_{l}\left( t_{s} \right)}{\delta\left( {t - t_{l,s}} \right)}}}} + {\sum\limits_{f}{\left( {V_{reset} - {V\left( t_{f} \right)}} \right){\delta\left( {t - t_{f}} \right)}}}}$

T_(m) is the characteristic membrane time of the artificial neuronconsidered; I indexes each incoming synapse, of weight w, of theartificial neuron considered; s indexes the spikes received by theartificial neuron considered by each synapse i, with their arrival timet_(i,s); f indexes the spikes emitted by the artificial neuronconsidered with their emission time t_(f).

The values of the characteristic time T_(m) and the threshold value Thare chosen as a function of the layer considered. The choice of thethreshold value depends on the number of spikes expected for the layerconsidered.

For each artificial neuron n13 of the intermediate layer:

-   -   the characteristic membrane time T_(m) is preferentially        comprised in the interval [dt; 6*dt]; generally speaking, since        the artificial neurons n13 of the intermediate layer learn        portions, at a given instant, of waveform of action potentials,        preferentially for the artificial neurons n13 of the        intermediate layer a characteristic time T_(m) of the same order        of magnitude as the sampling period dt is chosen;    -   the threshold value Th is chosen so as to be slightly greater        than the potential of the artificial neurons when the electrical        signal only contains noise;    -   the reset value VRESET is preferentially comprised in the        interval [−100*Th; 0].

According to a particular exemplary embodiment, for each artificialneuron n13 of the intermediate layer:

-   -   the characteristic membrane time T_(m) is equal to 3*dt;    -   the threshold value Th is equal to Nt*overlap*0.75 with Nt the        number of columns of the input layer and “overlap” the overlap        of the sensitivity intervals Sen of the artificial neurons of        the input layer    -   which is set at 8 in the particular example of FIG. 3 c;    -   the reset value V_(RESET) is equal to −20*Th.

For each artificial neuron n15 of the output layer:

-   -   the characteristic membrane time T_(m) is preferentially        comprised in the interval [1 ms; 4 ms]; generally speaking,        since the role of each artificial neuron n15 of the output layer        is to learn the whole of an action potential, the characteristic        time T_(m) of the artificial neurons n15 of the output layer is        preferentially chosen of the order of the duration of an action        potential;    -   the reset value V_(RESET) is preferentially comprised in the        interval [−20*Th; 0].

According to a particular exemplary embodiment, for each artificialneuron n15 of the output layer:

-   -   the characteristic membrane time T_(m) is equal to 2.5 ms;    -   the reset value V_(RESET) is equal to −5*Th.

It is advantageously provided that each artificial neuron of theintermediate layer, after having emitted a spike, is prevented fromemitting another spike during a refractory period. This refractoryperiod is typically of the order of magnitude of the duration of asampling period dt and preferentially comprised in the interval [dt;10*dt]. In the particular exemplary embodiment, the refractory period is5*dt. Similarly, it is advantageously provided that each artificialneuron of the output layer, after having emitted a spike, is preventedfrom emitting another spike for a second refractory period. This secondrefractory period is typically of the order of magnitude of the durationof an action potential, preferentially comprised between 0.5 ms and 10ms and more preferentially comprised between 1 ms and 4 ms. In theparticular exemplary embodiment, the refractory period is 2.5 ms. Theweight of each first excitatory synapse se1 is preferentiallynormalized: the weight of each first excitatory synapse se1 then belongsto the interval [0; 1]. The weight of each second excitatory synapse se2is preferentially normalized: the weight of each second excitatorysynapse se2 then belongs to the interval [0; 1].

Each excitatory synapse, that is to say each first excitatory synapsese1 and each second excitatory synapse se2 in the case of the network ofartificial neurons 10, advantageously respects a STDP rule whichmodifies its weight as a function of the instants at which thepresynaptic spikes and the postsynaptic spikes respectively occur.Typically, for each excitatory synapse, a coincidence time window Δtbetween presynaptic and postsynaptic spikes is defined:Δt=−[−T _(stdp−) ; +T _(stdp+)]

where T_(stdp−); is a duration measured upstream of each presynapticspike received by said excitatory synapse and T_(stdp+) is a durationmeasured downstream of each presynaptic spike received by saidexcitatory synapse.

This coincidence time window is preferentially chosen as a function ofthe positioning of each excitatory synapse within the network ofartificial neurons. For each first excitatory synapse si1:

-   -   T_(stdp+) belongs preferentially to the interval [0; 3*dt] and        in the particular exemplary embodiment, T_(stdp+) is equal to        1*dt;    -   T_(stdp−) belongs preferentially to the interval [0; 3*dt] and        in the particular exemplary embodiment, T_(stdp−) is equal to 0.

For each second excitatory synapse si2:

-   -   T_(stdp+) belongs preferentially to the interval [1 ms; 3 ms]        and in the particular exemplary embodiment, T_(stdp+) is equal        to 1.5 ms;    -   T_(stdp−) belongs preferentially to the interval [1 ms; 3 ms]        and in the particular exemplary embodiment, T_(stdp−) is equal        to 1.5 ms.

Advantageously a “winner takes all” type mechanism is used within theintermediate layer 13 and within the output layer 15. This mechanism isillustrated in FIGS. 4a and 4b , which are described jointly. Accordingto this mechanism, each artificial neuron n13 of the intermediate layeris connected to all the other artificial neurons n13 of the intermediatelayer by a plurality of first inhibitory synapses sit. Similarly, eachartificial neuron n15 of the output layer is connected to all the otherartificial neurons n15 of the output layer by a plurality of secondinhibitory synapses si2. Thus, an artificial neuron emitting a spike ata given instant laterally inhibits the other neurons of the same layerin order to prevent them from emitting, also, a spike at the sameinstant.

This lateral inhibition contributes such that the artificial neurons ofthe intermediate and output layers learn to emit spikes for differentinput waveforms. It is in fact possible that several artificial neuronsof a same layer have a tendency to learn the same waveforms. In thiscase, the lateral inhibition constrains these artificial neurons not toemit their spikes exactly at the same moment, thus to shift theiremissions while respecting a certain latency delay. The latency delay isdetermined by the configuration of the lateral inhibition: the higherthe lateral inhibition, the greater the latency delay. Thus, thanks tothe lateral inhibition, the artificial neurons of a same layer learneither to emit spikes for different input action potentials, or to emitspikes for different parts of a same input action potential. The weightof each first inhibitory synapse si1 is preferentially comprised in theinterval [0.1*Th; 0.5*Th], with Th the threshold value of eachartificial neuron n13 of the intermediate layer. In the particularexemplary embodiment, the weight of each first inhibitory synapse si1 isequal to 0.2*Th.

The weight of each second inhibitory synapse si2 is preferentiallycomprised in the interval [1*Th; 10*Th], with Th the threshold value ofeach artificial neuron n15 of the output layer. In the particularexemplary embodiment, the weight of each second inhibitory synapse si2is equal to 10*Th.

An STDP (spike-timing-dependent plasticity) rule may also be implementedfor each inhibitory synapse, that is to say for each first inhibitorysynapse si1 and for each second inhibitory synapse si2 in the case ofthe network of artificial neurons 10, according to which;

-   -   the weight of each inhibitory synapse increases in the event of        coincidence of a postsynaptic spike and a presynaptic spike in a        certain time window, and    -   the weight of each inhibitory synapse decreases in the case of a        presynaptic spike only in the time window considered.

In the case of a postsynaptic spike only in the time window considered,the weight of each inhibitory synapse may remain unchanged.Alternatively, the weight of each inhibitory synapse may decrease in theevent of a postsynaptic spike only in the time window considered.

In addition to the mechanism of lateral inhibition of “winner take all”type that has been described, each second excitatory synapse se2advantageously respects a STDP rule that modifies its weight as afunction of the instants at which take place respectively thepresynaptic spikes and the lateral inhibitions. Alternatively, said STDPrule may be implemented both for the first excitatory synapses se1 andfor the second excitatory synapses se2, or only for the first excitatorysynapses se1. Typically, for each excitatory synapse, a coincidence timewindow between excitation and inhibition is defined, as describedpreviously.

According to an embodiment, the STDP rule implemented for eachexcitatory synapse is the following:

-   -   the weight of an excitatory synapse remains unchanged when its        predefined time window comprises a presynaptic spike only;    -   the weight of an excitatory synapse is decreased, for example by        a quantity a_(post), when its predefined time window comprises a        postsynaptic spike only;    -   the weight of an excitatory synapse is increased, for example by        a quantity (a_(pair)−a_(post)), when its predefined time window        comprises a presynaptic spike and a postsynaptic spike.

According to this embodiment, the weight of each excitatory synapseremains comprised between 0 and a maximum value that is typically 1 fornormalized weight.

Alternatively, the weight of an excitatory synapse may only be increasedwhen its predefined time window comprises a postsynaptic spikesucceeding a presynaptic spike. According to this alternative, when thepredefined time window comprises a presynaptic spike succeeding apostsynaptic spike, the weight of the excitatory synapse consideredremains unchanged or is decreased.

For each artificial neuron n13 of the intermediate layer, the quantitya_(pair) is preferentially comprised in the interval [0.001; 0.01] andthe quantity a_(post) is preferentially comprised in the interval[0.4*a_(pair); 0.8*a_(pair)]. In the particular exemplary embodiment,for each artificial neuron n13 of the intermediate layer, the quantitya_(pair) is 0.003 and the quantity a_(post) is 0.65*a_(pair).

For each artificial neuron n15 of the output layer, the quantitya_(pair) is preferentially comprised in the interval [0.001; 0.02] andthe quantity a_(post) is preferentially comprised in the interval[0.4*a_(pair); 0.7*a_(pair)]. In the particular exemplary embodiment,for each artificial neuron n15 of the output layer, the quantitya_(pair) is 0.01 and the quantity a_(post) is 0.5*a_(pair).

According to another embodiment, the STDP rule implemented for eachexcitatory synapse is the following:

-   -   when an artificial neuron of the intermediate layer n13 or the        output layer n15 receives, in the predefined coincidence time        window between excitation and inhibition, a spike transmitted by        an excitatory synapse and a lateral inhibition transmitted by        another artificial neuron of the same layer, the weight of said        excitatory synapse is decreased by a quantity (a_(lat)−a_(pre));    -   when an artificial neuron of the intermediate layer n13 or the        output layer n15 receives, in the predefined coincidence time        window between excitation and inhibition, a spike transmitted by        an excitatory synapse and no lateral inhibition transmitted by        another artificial neuron, the weight of said excitatory synapse        is increased by a quantity a_(pre).

For each artificial neuron n15 of the output layer, the quantity a_(lat)is preferentially comprised in the interval [0; 0.2*a_(pair)] and thequantity a_(pre) is preferentially comprised in the interval [0;0.5*a_(lat)]. In the particular exemplary embodiment, for eachartificial neuron n15 of the output layer, the quantity a_(lat) is0.1*a_(pair) and the quantity a_(pre) is 0.01*a_(pair).

According to another embodiment, the two STDP rules that have beendescribed may be implemented simultaneously. In this case, eachexcitatory synapse has a first predefined time window for theimplementation of the first STDP rule and a second predefined timewindow for the implementation of the second STDP rule, and the first andsecond predefined time windows for each excitatory synapse may beidentical or distinct.

The number of artificial neurons n13 of the intermediate layer is chosensufficiently large so that all possible patterns can be learnt. Thenumber of artificial neurons n13 of the intermediate layer thus dependson the number of different types of action potentials to detect and thelatency delay configured for the intermediate layer 13. A too highnumber of artificial neurons n13 does not modify the operation of thenetwork of artificial neurons but has a drawback in terms of computingtime. A too low number of artificial neurons n13 limits thepossibilities of learning patterns. In practice, the number ofartificial neurons n13 of the intermediate layer is preferentiallycomprised in the interval [30; 200]. In the particular exemplaryembodiment, the intermediate layer comprises 80 artificial neurons n13.

The number of artificial neurons n15 of the output layer is chosengreater than or equal to the number of different types of actionpotentials to detect. In practice, since the number of action potentialsto detect is not generally known in advance, the number of artificialneurons n15 of the output layer is preferentially comprised in theinterval [3; 30] and more preferentially comprised in the interval [7;15], In the particular exemplary embodiment, the output layer comprises10 artificial neurons n15.

The artificial neurons n13 of the intermediate layer advantageouslyrespect a STP (short term plasticity) rule which will now be described.The role of the artificial neurons n11 of the input layer is to convertthe electrical signal dln into a form that is exploitable by theartificial neurons n13 of the intermediate layer. The artificial neuronsn11 of the input layer thus convert the electrical signal dln into atrain of first spikes. The role of the artificial neurons n13 of theintermediate layer is next to learn to recognize waveforms or parts ofwaveforms. To do so, it is wished that the artificial neurons n13 of theintermediate layer manage to filter noise in order that they learn torecognize noise. The short term plasticity rule STP contributes to thisobjective.

Each first excitatory synapse se1, which connects an artificial neuronn11 of the input layer, designated presynaptic artificial neuron, to anartificial neuron n13 of the intermediate layer, designated postsynapticartificial neuron, is considered. According to the STP rule, the weightof each first excitatory synapse se1 is allotted a synaptic coefficientP_(rel) such that 0≤P_(rel)≤1.

Each postsynaptic artificial neuron n13 receiving a spike via a firstexcitatory synapse se1 is excited proportionally to the product of thesynaptic coefficient P_(rel) and the weight of said first excitatorysynapse. The synaptic coefficient P_(rel) decreases when the presynapticartificial neuron n11 emits a spike, and the synaptic coefficientP_(rel) increases towards 1 otherwise. According to one embodiment, thesynaptic coefficient respects the following equation:

$\frac{{dP}_{rel}}{dt} = {{\frac{1}{\tau_{stp}}\left( {1 - P_{rel}} \right)} - {\sum\limits_{s}{{P_{rel} \cdot f_{d}}{\delta\left( {t - t_{s}} \right)}}}}$

Where s indexes the presynaptic spikes, that is to say the spikesemitted by the presynaptic artificial neurons n11, each presynapticspike taking place at an instant t_(s). Each time that a postsynapticartificial neuron n13 receives a spike via a first excitatory synapsese1, the synaptic coefficient P_(rel) of said first excitatory synapsese1 is decreased by the quantity P_(rel)*f_(d), where f_(d) is thedegree of depression. The degree of depression f_(d) is chosen such thatan artificial neuron n11 of the input layer that discharges at each timestep has a low synaptic coefficient P_(rel). When the first excitatorysynapse se1 does not transmit any spike, its synaptic coefficientP_(rel) tends towards 1 in a characteristic time T_(stp). Thecharacteristic time T_(stp) is preferentially comprised between 0.1 msand 10 ms and more preferentially comprised between 0.5 ms and 3 ms. Thecharacteristic time T_(stp) is typically of the order of magnitude ofthe duration of an action potential. In the particular exemplaryembodiment, the characteristic time T_(stp) is equal to 1.5 ms. In theparticular exemplary embodiment, the degree of depression f_(d) ischosen such that:

$f_{d} = {1 - {\exp\left( {{- 6.5}*\frac{dt}{\tau_{stp}}} \right)}}$

The short term plasticity rule STP uses the fact that the artificialneurons n11 of the input layer associated with the noise amplitudevalues have a tendency to emit spikes permanently: thanks to the shortterm plasticity rule STP, the more an artificial neuron n11 of the inputlayer emits spikes, the more the excitation capacity of each firstexcitatory synapse se1 connecting this artificial neuron n11 of theinput layer to the artificial neurons n13 of the intermediate layerdecreases. According to the LIF model that is used to define thebehavior of the artificial neurons n13 of the intermediate layer, thepotential of each artificial neuron n13 then increases during thereception of spikes via excitatory synapses, and tends towards a restvalue otherwise. When the electrical signal dln only contains noise,which is converted by the input layer 11 into a train of first spikes,constant, and relatively low because P_(rel) is low, and the potentialof the artificial neurons n13 of the intermediate layer stabilizesaround a value greater than the rest value. The threshold of theartificial neurons n13 of the intermediate layer is chosen greater thanthis stabilization value, in order that the artificial neurons n13 ofthe intermediate layer do not emit a spike when they receive noise. Atthe same time, the threshold of the artificial neurons n13 of theintermediate layer is chosen in such a way that the increase inpotential linked to the arrival of an action potential, and thus to theemission by the input layer of a series of spikes with a greaterexcitation capacity because P_(rel) is large, leads to the emission ofat least one spike.

The different action potentials to detect and to sort generally havedifferent durations and different amplitudes. Consequently, two distinctaction potentials typically lead to the activation of different groupsof artificial neurons n11 of the input layer and the transmission to theartificial neurons n13 of the intermediate layer then to the artificialneurons n15 of the output layer of trains of spikes of different sizes,that is to say not comprising the same number of spikes. The spikeemission threshold of the artificial neurons n15 of the output layermust be configured sufficiently low so that waveforms of short duration,for which the number of spikes emitted by the artificial neurons of theintermediate layer n13 is low, can be detected. However, if the spikeemission threshold of the artificial neurons n15 of the output layer isdefined at a low value making it possible to detect waveforms of shortduration, the artificial neurons n15 of the output layer which learn torecognize waveforms of long duration corresponding to trains of spikesof large size are going to emit spikes before the trains of spikes havefinished being transmitted to them by the artificial neurons n13 of theintermediate layer. In this case, since each long train of spikes isgoing to stop being transmitted after an artificial neuron n15 of theoutput layer has emitted a spike, another artificial neuron n15 of theoutput layer is going to be able to learn to recognize the end of thewaveform corresponding to the long train of spikes. In order to preventthis undesirable behavior, it is possible to define a high lateralinhibition.

Nevertheless, a too high lateral inhibition is not desirable becausedifferent action potentials may take place one after the other in ashort time interval: in such a case, it is wished that the artificialneurons n15 of the output layer are capable of emitting spikes one afterthe other in a sufficiently short time interval. In addition, even if asufficiently high lateral inhibition is defined to guarantee that asingle artificial neuron n15 of the output layer does not emit a spikefor a given waveform, only the start of the long trains of spikes willbe taken into account, which will prevent differentiating two waveformsbefore an identical start and a different end.

It is desired that the sorting method according to one aspect of theinvention is robust to such variations of amplitude and duration ofaction potentials, in order that the output layer 15 still only emits asingle spike for each occurrence of each type of action potentialdetected while being capable of detecting all the types of actionpotential, independently of their length.

To do so, a plasticity rule is advantageously introduced on the spikeemission threshold Th of each artificial neuron n15 of the output layer,in order that the spike emission threshold of each artificial neuron n15of the output layer adapts to the waveform that it is in the course oflearning, and thus the size of the train of spikes corresponding to thewaveform that it is in the course of learning. When a plasticity rule isimplemented on the threshold Th of each artificial neuron n15 of theoutput layer 15, the initial threshold Th is preferentially chosen verylow, that is to say for example equal to 1. The threshold Th is thenadjusted as a function of its plasticity rule. In the absence ofimplementation of such a plasticity rule, the threshold Th of eachartificial neuron n15 of the output layer 15 is preferentially chosen inthe interval [3; 10]. Two possible implementations of the plasticityrule on the threshold Th of each artificial neuron of the output layerwill now be described.

According to a first alternative embodiment, a time window is definedaround each postsynaptic spike emitted by an artificial neuron n15 ofthe output layer and the plasticity rule on the spike emission thresholdof each artificial neuron n15 of the output layer is the following:

-   -   the threshold value of each artificial neuron n15 of the output        layer emitting a spike at an instant t is increased        proportionally to the number of spikes Ni received by said        artificial neuron n15 in the time window defined:        Th(t)=Ni*Δ _(Th+);    -   the threshold value of each artificial neuron n15 of the output        layer emitting a spike at an instant t1 is decreased in such a        way that:        Th(t2)=α*Th(t1)        with Th(t1) the threshold value at the instant t1, Th(t2) the        threshold value at an instant t2 later than the instant t1 and α        a real number such that 0<α<1.

α belongs preferentially to the interval [0.95; 0.999]; in theparticular exemplary embodiment, αis equal to 0.99. The time windowaround the instant t may be comprised between 0.1 ms and 20 ms,preferentially between 1 and 3 ms, and is typically 2 ms around theinstant t.

α_(Th+) belongs preferentially to the interval [0.5*(1−α); 0.8*(1−α)].In the particular exemplary embodiment, Δ_(Th+) is equal to 0.6*(1−α).

Consequently, when a given action potential takes place, the artificialneuron n15 of the output layer learning to recognize this actionpotential receives a train of N presynaptic spikes, which leads to anincrease in its spike emission threshold proportional to N, and emits apostsynaptic spike, which leads to a reduction in its spike emissionthreshold proportional to the value of the spike emission threshold. Thespike emission threshold thus tends towards a value that is proportionalto the average number of presynaptic spikes. It is desired that amajority of presynaptic spikes is taken into account before emitting apostsynaptic spike. It may however happen that certain presynapticspikes, normally present, are missing. In order to be able to emit apostsynaptic spike even if only a part of the presynaptic spikesexpected is present, the spike emission threshold thus must not be toohigh. It thus involves finding a compromise between taking into accountthe majority of presynaptic spikes and being robust to potential errorsof the intermediate layer 13. In practice, a spike emission threshold ispreferentially chosen equal to between 0.3 and 0.8 times the averagenumber of presynaptic spikes emitted during the occurrence of an actionpotential.

According to a second alternative embodiment, a first time window isdefined before each postsynaptic spike and a second time window aftereach postsynaptic spike, and the plasticity rule on the spike emissionthreshold of each artificial neuron n15 of the output layer is thefollowing;

-   -   when an artificial neuron n15 of the output layer receives a        presynaptic spike in the first predefined time window, the spike        emission threshold of said artificial neuron n15 of the output        layer is decreased;    -   when an artificial neuron n15 of the output layer receives a        presynaptic spike in the second predefined time window, the        spike emission threshold of said artificial neuron n15 of the        output layer is increased.

The first time window before each postsynaptic spike may be comprisedbetween 0.1 ms and 20 ms, preferentially between 1 and 3 ms, and istypically 2 ms. The second time window after each postsynaptic spike maybe comprised between 0.1 ms and 20 ms, preferentially between 1 and 3ms, and is typically 2 ms.

Consequently, the spike emission threshold of each artificial neuron n15of the output layer adapts in such a way that each artificial neuron n15of the output layer emits a postsynaptic spike after having received anumber of presynaptic spikes proportional to the total number ofpresynaptic spikes received for the duration of the correspondingwaveform. As previously, it involves finding a compromise between takinginto account the majority of presynaptic spikes and being robust topotential errors of the intermediate layer 13. In practice, a spikeemission threshold equal to between 0.3 and 0.8 times the totality ofthe presynaptic spikes emitted during the occurrence of an actionpotential is preferentially chosen.

In relation with FIGS. 5 to 8, several alternative embodiments ofnetworks of artificial neurons will now be described for theimplementation of the method 100 for unsupervised sorting, in real time,of action potentials of a plurality of biological neurons according toone aspect of the invention. FIG. 5 schematically shows a second networkof artificial neurons 20 for the implementation of the method 100according to one aspect of the invention, comprising two intermediatelayers in parallel. The second network of artificial neurons 20comprises:

-   -   the input layer 11 comprising the plurality of artificial        neurons n11,    -   the intermediate layer 13 comprising the plurality of artificial        neurons n13,    -   a second intermediate layer 14 comprising a plurality of        artificial neurons n14, and    -   the output layer 15 comprising the plurality of artificial        neurons n15.

The plurality of first excitatory synapses se1 connects each artificialneuron of the input layer n11 to the plurality of artificial neurons ofthe intermediate layer n13 and to the plurality of artificial neurons ofthe second intermediate layer n14. The plurality of second excitatorysynapses se2 connects each artificial neuron of the intermediate layern13 to the plurality of artificial neurons of the output layer n15. Asecond plurality of second excitatory synapses se22 connects eachartificial neuron of the second intermediate layer n14 to the pluralityof artificial neurons of the output layer n15.

The input layer 11 transmits the train of first spikes to theintermediate layer 13 and to the second intermediate layer 14 via theplurality of first excitatory synapses se1. The intermediate layer 13converts the train of first spikes into a train of second spikes andtransmits the train of second spikes to the output layer 15 via theplurality of second excitatory synapses se2. The second intermediatelayer 14 converts the train of first spikes into a second train ofsecond spikes and transmits the second train of second spikes to theoutput layer 15 via the second plurality of second excitatory synapsesse22. The output layer then uses the train of second spikes and thesecond train of second spikes to sort each occurrence of each type ofaction potential present in the electrical signal dln.

FIG. 6 schematically shows a third network of artificial neurons 30 forthe implementation of the method 100 according to one aspect of theinvention, comprising two input layers in parallel. The third network ofartificial neurons comprises:

-   -   the input layer 11 comprising the plurality of artificial        neurons n11,    -   a second input layer 12 comprising a plurality of artificial        neurons n12,    -   the intermediate layer 13 comprising the plurality of artificial        neurons n13 and    -   the output layer 15 comprising the plurality of artificial        neurons n15.

The plurality of first excitatory synapses se1 connects each artificialneuron of the input layer n11 to the plurality of artificial neurons ofthe intermediate layer n13. A second plurality of first excitatorysynapses se12 connects each artificial neuron of the second input layern12 to the plurality of artificial neurons of the intermediate layern13.

The plurality of second excitatory synapses se2 connects each artificialneuron of the intermediate layer n13 to the plurality of artificialneurons of the output layer n15.

The input layer 11 receives the electrical signal din and the secondinput layer 30 receives a second electrical signal dln2. The secondelectrical signal dln2 measures an electrical activity of a secondplurality of biological neurons and has a variable amplitude as afunction of action potentials emitted by the plurality of secondbiological neurons over time. The second electrical signal dln2 may bedifferent from the electrical signal dln or identical to the electricalsignal dln. The second plurality of biological neurons of which theelectrical activity is measured by the second electrical signal dln2 maybe partially or totally different from the plurality of biologicalneurons of which the electrical activity is measured by the electricalsignal dln. Alternatively, the second plurality of biological neurons ofwhich the electrical activity is measured by the second electricalsignal dln2 may be identical to the plurality of biological neurons ofwhich the electrical activity is measured by the electrical signal dln.The input layer 11 converts the amplitude of the first electrical signaldln into a train of first spikes and transmits the train of first spikesto the intermediate layer 13 via the plurality of first excitatorysynapses se1. The second input layer 12 converts the amplitude of thesecond electrical signal dln2 into a second train of first spikes 15 andtransmits the second train of first spikes to the intermediate layer 13via the second plurality of first excitatory synapses se2. Theintermediate layer 13 converts the train of first spikes and the secondtrain of first spikes into a train of second spikes and transmits thetrain of second spikes to the output layer 15 via the plurality ofsecond excitatory synapses se2. The output layer 15 then uses the trainof second spikes to sort each occurrence of each type of actionpotential present in the electrical signal dln and in the secondelectrical signal dln2.

FIG. 7 schematically shows a fourth network of artificial neurons 40 forthe implementation of the method 100 according to one aspect of theinvention, comprising two input layers in parallel, each input layerbeing associated with its own intermediate layer. The fourth network ofartificial neurons 40 comprises:

-   -   the input layer 11 comprising the plurality of artificial        neurons n11,    -   the second input layer 12 comprising the plurality of artificial        neurons n12,    -   the intermediate layer 13 comprising the plurality of artificial        neurons n13,    -   the second intermediate layer 14 comprising the plurality of        artificial neurons n14, and    -   the output layer 15 comprising the plurality of artificial        neurons n15.

The plurality of first excitatory synapses se1 connects each artificialneuron of the input layer n11 to the plurality of artificial neurons ofthe intermediate layer n13. A second plurality of first excitatorysynapses se12 connects each artificial neuron of the second input layern12 to the plurality of artificial neurons of the second intermediatelayer n14. The plurality of second excitatory synapses se2 connects eachartificial neuron of the intermediate layer n13 to the plurality ofartificial neurons of the output layer n15. A second plurality of secondexcitatory synapses se22 connects each artificial neuron of the secondintermediate layer n14 to the plurality of artificial neurons of theoutput layer n15.

The input layer 11 receives the electrical signal dln and the secondinput layer receives the second electrical signal dln2. The electricalsignal dln and the second electrical signal dln2 have been describedpreviously. The input layer 11 converts the amplitude of the firstelectrical signal dln into a train of first spikes and transmits thetrain of first spikes to the intermediate layer 13 via the plurality offirst excitatory synapses se1. The second input layer 12 converts theamplitude of the second electrical signal dln2 into a second train offirst spikes and transmits the second train of first spikes to thesecond intermediate layer 14 via the second plurality of firstexcitatory synapses se12. The intermediate layer 13 converts the trainof first spikes into a train of second spikes and transmits the train ofsecond spikes to the output layer 15 via the plurality of secondexcitatory synapses se2. The second intermediate layer 14 converts thesecond train of first spikes into a second train of second spikes andtransmits the second train of second spikes to the output layer 15 viathe second plurality of second excitatory synapses se22. The outputlayer 15 then uses the train of second spikes and the second train ofsecond spikes to sort each occurrence of each type of action potentialpresent in the electrical signal dln and in the second electrical signaldln2.

FIG. 8 schematically shows a fifth network of artificial neurons 50 forthe implementation of the method 100 according to the method of theinvention, comprising two intermediate layers in series. The fifthnetwork of artificial neurons 50 comprises:

-   -   the input layer 11 comprising the plurality of artificial        neurons n11,    -   the intermediate layer 13 comprising the plurality of artificial        neurons n13,    -   a second intermediate layer 13′ comprising a plurality of        artificial neurons n13′,    -   the output layer 15 comprising the plurality of artificial        neurons n15.

The plurality of first excitatory synapses se1 connects each artificialneuron of the input layer n11 to the plurality of artificial neurons ofthe intermediate layer n13. A plurality of second excitatory synapsesse2′ connects each artificial neuron of the intermediate layer n13 tothe plurality of artificial neurons of the second intermediate layern13′. A plurality of third excitatory synapses se3 connects eachartificial neuron of the second intermediate layer n13′ to the pluralityof artificial neurons of the output layer n15.

The input layer 11 converts the amplitude of the first electrical signaldln into a train of first spikes and transmits the train of first spikesto the intermediate layer 13 via the plurality of first excitatorysynapses se1. The intermediate layer 13 converts the train of firstspikes into a train of second spikes and transmits the train of secondspikes to the second intermediate layer 13′ via the plurality of secondexcitatory synapses se2′.

The second intermediate layer 13′ converts the train of second spikesinto a train of third spikes and transmits the train of third spikes tothe output layer 15 via the plurality of third excitatory synapses se3.The output layer 15 then uses the train of third spikes to sort eachoccurrence of each type of action potential present in the electricalsignal dln.

The invention claimed is:
 1. A method for unsupervised sorting, in realtime, of action potentials of a plurality of biological neurons by anetwork of artificial neurons implemented on a neuromorphic circuit, thenetwork of artificial neurons comprising an input layer, an intermediatelayer and an output layer, each artificial neuron of the input layerbeing connected to a plurality of artificial neurons of the intermediatelayer by a plurality of first excitatory synapses and each artificialneuron of the intermediate layer being connected to a plurality ofartificial neurons of the output layer by a plurality of secondexcitatory synapses, at least one first or second excitatory synapseconnecting a first artificial neuron to a second artificial neuron andhaving a weight that is modified as a function of the instants at whichtake place presynaptic spikes emitted by the first artificial neuron andpostsynaptic spikes emitted by the second artificial neuron, the methodcomprising: receiving by the input layer an electrical signal measuringan electrical activity of a plurality of biological neurons, theelectrical signal having a variable amplitude as a function of actionpotentials emitted by the plurality of biological neurons over time, theelectrical signal measuring the electrical activity of the plurality ofbiological neurons being directly received by the input layer such thatthe electrical signal is fed to the input layer without being previouslyencoded or stored outside of said neuromorphic circuit, or both;converting by the input layer the amplitude of the electrical signalinto a train of first spikes; transmitting by the input layer the trainof first spikes to the intermediate layer; converting by theintermediate layer the train of first spikes into a train of secondspikes; transmitting by the intermediate layer the train of secondspikes to the output layer; as a function of the train of second spikes,sorting by the output layer each occurrence of each type of actionpotential present in the electrical signal.
 2. The method according toclaim 1, wherein, as a function of the train of second spikes, theoutput layer sorts each occurrence of each type of action potentialpresent in the electrical signal by activating at the most a singlegroup of artificial neurons of the output layer for each occurrence ofan action potential in the electrical signal, each group of artificialneurons of the output layer comprising at least one artificial neuron ofthe output layer and being associated with a single type of actionpotential and each type of action potential being associated with asingle group of artificial neurons of the output layer.
 3. The methodaccording to claim 2, wherein the input layer is a matrix of artificialneurons having: Na lines, the number Na of lines being chosen as afunction of a range of values in which the amplitude of the electricalsignal is variable, in such a way that the artificial neurons of a sameline are activated for a same amplitude value of the electrical signal,and Nt columns, the number Nt of columns being chosen as a function of atime frame for observing the electrical signal, in such a way that theartificial neurons of a same column receive the electrical signal at asame given instant; wherein, at each instant t_(n)=n*dt, with n anatural integer and dt a time step: a first column C₀ of artificialneurons receives the electrical signal, and as a function of theamplitude value of the electrical signal received, at least oneartificial neuron of the first column C₀ emits a spike that istransmitted to the intermediate layer.
 4. The method according to claim3, wherein a margin is defined around each amplitude value of theelectrical signal received in such a way that, at each instantt_(n)=n*dt: the first column Co of artificial neurons receives theelectrical signal, and as a function of the amplitude value of theelectrical signal received and of the margin defined around saidamplitude value, at least two artificial neurons of the first column C₀each emit a spike, each spike being transmitted to the intermediatelayer.
 5. The method according to claim 3, wherein the number of columnsNt is strictly greater than 1 and wherein, at each instantt_(k)=t_(n)+k*dt′, with dt′ a second time step, and for each columnC_(k) of artificial neurons, with k a natural integer such that1≤k≤Nt−1, each artificial neuron of same line as an artificial neuron ofthe first column C₀ having emitted a spike at the instant t_(n), emitsin its turn a spike that is transmitted to the intermediate layer. 6.The method according to claim 1, wherein: each artificial neuron of theinput layer is connected to a plurality of artificial neurons of theintermediate layer by the plurality of first excitatory synapses in sucha way that a spike emitted by said artificial neuron of the input layeris transmitted to the plurality of artificial neurons of theintermediate layer by the plurality of first excitatory synapses; eachartificial neuron of the intermediate layer is connected to a pluralityof artificial neurons of the output layer by the plurality of secondexcitatory synapses in such a way that a spike emitted by saidartificial neuron of the intermediate layer is transmitted to theplurality of artificial neurons of the output layer by the plurality ofsecond excitatory synapses; each artificial neuron of the intermediatelayer and each artificial neuron of the output layer have a potentialhaving initially a value designated “rest value”; when an excitatorysynapse transmits a spike to an artificial neuron of the intermediatelayer or of the output layer, the potential of said artificial neuronincreases proportionally to the weight of said first excitatory synapse;when the potential of an artificial neuron of the intermediate layer orof the output layer exceeds a threshold value, said artificial neuronemits a spike and its potential is reduced to a reset value; in theabsence of spike at the input of an artificial neuron of theintermediate layer or of the output layer and when said neuron does notemit a spike itself, the potential of said neuron returns to its restvalue in a characteristic time τ_(m).
 7. The method according to claim6, wherein the weight of each excitatory synapse is modified as afunction of a predefined time window: for a given excitatory synapse,when the predefined time window comprises a presynaptic spike and apostsynaptic spike, the weight of this excitatory synapse is increased;for a given excitatory synapse, when the predefined time windowcomprises a postsynaptic spike only, the weight of this excitatorysynapse is decreased; for a given excitatory synapse, when thepredefined time window comprises a presynaptic spike only, the weight ofthis excitatory synapse remains unchanged.
 8. The method according toclaim 1, wherein : the network of artificial neurons also comprises atleast one artificial detection neuron, each artificial neuron of theinput layer being connected to the artificial detection neuron by afirst excitatory detection synapse and the artificial detection neuronbeing connected to a plurality of artificial neurons of the intermediatelayer by a plurality of second excitatory detection synapses; each firstexcitatory detection synapse has a weight allotted a synapticcoefficient P_(rel) such that 0≤P_(rel)≤1, the synaptic coefficientP_(rel) decreasing when the presynaptic artificial neuron emits a spike,and the synaptic coefficient P_(rel) increasing towards 1 otherwise witha characteristic time τ_(stp); the artificial detection neuron receivinga spike via a first excitatory detection synapse is excitedproportionally to the product of the synaptic coefficient P_(rel) andthe weight of said first excitatory detection synapse.
 9. The methodaccording to claim 1, wherein : each artificial neuron of theintermediate layer is connected to all of the other artificial neuronsof the intermediate layer by a plurality of first inhibitory synapses insuch a way that a spike emitted by said artificial neuron of theintermediate layer is transmitted to all of the other artificial neuronsof the intermediate layer by the plurality of first inhibitory synapses;each artificial neuron of the output layer is connected to all of theother artificial neurons of the output layer by a plurality of secondinhibitory synapses in such a way that a spike emitted by saidartificial neuron of the output layer is transmitted to all of the otherartificial neurons of the output layer by the plurality of secondinhibitory synapses; when an inhibitory synapse transmits a spike to anartificial neuron of the intermediate layer or of the output layer, saidartificial neuron is prevented from emitting a spike for a predefinedduration corresponding to an inhibition period and/or the potential ofsaid artificial neuron is decreased proportionally to the weight of saidinhibitory synapse.
 10. The method according to claim 9, wherein aplurality of second excitatory synapses connects each artificial neuronof the intermediate layer to a plurality of artificial neurons of theoutput layer, each second excitatory synapse having a weight, wherein:for each second excitatory synapse, when an artificial neuron of theoutput layer receives, in a predefined time window, a spike transmittedby said second excitatory synapse and a spike transmitted by a secondinhibitory synapse, then the weight of said second excitatory synapse isdecreased; for each second excitatory synapse, when an artificial neuronof the output layer receives, in the predefined time window, a spiketransmitted by said second excitatory synapse and no spike transmittedby a second inhibitory synapse, then the weight of said secondexcitatory synapse is increased.
 11. The method according to claim 1,wherein: each artificial neuron of the output layer has a potential;each artificial neuron of the output layer emits a spike when itspotential exceeds a threshold value; wherein: the threshold value ofeach artificial neuron of the output layer emitting a spike at aninstant t is increased proportionally to the number of spikes receivedby said artificial neuron in a time window around the instant t; thethreshold value Th of each artificial neuron of the output layeremitting a spike at an instant t1 is decreased in such a way that:Th(t2)=α*Th(t1) with Th(t1) the threshold value at the instant t1,Th(t2) the threshold value at an instant t2 later than t1 and α a realnumber such that 0<α<1.
 12. The method according to claim 1, wherein thenetwork of artificial neurons comprises the input layer, theintermediate layer, a second intermediate layer and the output layer,and according to which: the input layer transmits the train of firstspikes to the intermediate layer and to the second intermediate layer;the second intermediate layer converts the train of first spikes into asecond train of second spikes; the second intermediate layer transmitsthe second train of second spikes to the output layer; as a function ofthe train of second spikes and the second train of second spikes, theoutput layer sorts each occurrence of each type of action potentialpresent in the electrical signal.
 13. The method according claim 1,wherein the network of artificial neurons comprises the input layer, asecond input layer, the intermediate layer and the output layer, andaccording to which: the second input layer receives a second electricalsignal measuring an electrical activity of a second plurality ofbiological neurons, the second electrical signal having a variableamplitude as a function of action potentials emitted by the secondplurality of biological neurons over time; the second input layerconverts the amplitude of the second electrical signal into a secondtrain of first spikes; the second input layer transmits the second trainof first spikes to the intermediate layer; the intermediate layerconverts the train of first spikes and the second train of first spikesinto a train of second spikes.
 14. The method according to claim 1,wherein the network of artificial neurons comprises the input layer, asecond input layer, the intermediate layer, a second intermediate layerand the output layer, and according to which: the second input layerreceives a second electrical signal measuring an electrical activity ofa second plurality of biological neurons, the second electrical signalhaving a variable amplitude as a function of action potentials emittedby the second plurality of biological neurons over time; the secondinput layer converts the amplitude of the second electrical signal intoa second train of first spikes; the second input layer transmits thesecond train of first spikes to the second intermediate layer; thesecond intermediate layer converts the second train of first spikes intoa second train of second spikes; the second intermediate layer transmitsthe second train of second spikes to the output layer; as a function ofthe train of second spikes and of the second train of second spikes, theoutput layer sorts each occurrence of each type of action potentialpresent in the electrical signal.
 15. A network of artificial neuronsfor the implementation of a method for unsupervised sorting, in realtime, of action potentials of a plurality of biological neuronsimplemented on a neuromorphic circuit, the network of artificial neuronscomprising: an input layer for the reception of an electrical signalhaving a variable amplitude as a function of action potentials emittedby the plurality of biological neurons over time, the conversion of theelectrical signal into a train of first spikes and the transmission ofthe train of first spikes to an intermediate layer, the input layerbeing adapted to directly receive the electrical signal measuring theelectrical activity of the plurality of biological neurons such that theelectrical signal is received by the input layer without beingpreviously encoded or stored outside of said neuromorphic circuit, orboth; said intermediate layer for the conversion of the train of firstspikes into a train of second spikes and the transmission of the trainof second spikes to an output layer; said output layer for the sorting,as a function of the train of second spikes, of each occurrence of eachtype of action potential present in the electrical signal; eachartificial neuron of the input layer being connected to a plurality ofartificial neurons of the intermediate layer by a plurality of firstexcitatory synapses and each artificial neuron of the intermediate layerbeing connected to a plurality of artificial neurons of the output layerby a plurality of second excitatory synapses, at least one first orsecond excitatory synapse connecting a first artificial neuron to asecond artificial neuron and having a weight that is modified as afunction of the instants at which take place presynaptic spikes emittedby the first artificial neuron and postsynaptic spikes emitted by thesecond artificial neuron.